The transmit coil of a metal detector has self-inductance

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic induction and alternating-current circuits · Electromagnetic induction and alternating-current circuits

Electricity, Magnetism and Electromagnetism, Ch Transients: RC, RL and LC circuits

Problem

L = 330\,\mu\mathrm{H}

. It is to be made to ring at as close to

100.0\,\mathrm{kHz}

as possible by connecting a capacitance across it; the coil's resistance is small enough that the ringing frequency may be taken as the undamped natural frequency

\omega_0/2\pi

, and the capacitors are ideal. Only two capacitors are in the parts drawer:

10\,\mathrm{nF}

and

22\,\mathrm{nF}

. The four possible tanks are: the

10\,\mathrm{nF}

alone, the

22\,\mathrm{nF}

alone, the two in series, and the two in parallel. ((a)) What capacitance would give exactly

100.0\,\mathrm{kHz}

with this coil? ((b)) Which of the four options comes closest to that capacitance? Give its capacitance. ((c)) What natural frequency does the chosen option actually give, and by what percentage does it miss

100.0\,\mathrm{kHz}

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